Hest {spatstat} | R Documentation |
Estimates the spherical contact distribution function of a random set.
Hest(X, ...)
X |
The observed random set.
An object of class "ppp" , "psp" or "owin" .
|
... |
Arguments passed to as.mask
to control the discretisation. |
The spherical contact distribution function
of a stationary random set X
is the cumulative distribution function H of the distance
from a fixed point in space to the nearest point of X,
given that the point lies outside X.
That is, H(r) equals
the probability that X
lies closer than r units away
from the fixed point x, given that X
does not cover x.
For a point process, the spherical contact distribution function
is the same as the empty space function F discussed
in Fest
.
For Hest
, the argument X
may be a point pattern
(object of class "ppp"
), a line segment pattern
(object of class "psp"
) or a window (object of class
"owin"
). It is assumed to be a realisation of a stationary
random set.
The algorithm first calls distmap
to compute the
distance transform of X
, then computes the Kaplan-Meier
and reduced-sample estimates of the cumulative distribution
following Hansen et al (1999).
An object of class "fv"
, see fv.object
,
which can be plotted directly using plot.fv
.
Essentially a data frame containing five columns:
r |
the values of the argument r at which the function H(r) has been estimated |
rs |
the ``reduced sample'' or ``border correction'' estimator of H(r) |
km |
the spatial Kaplan-Meier estimator of H(r) |
hazard |
the hazard rate lambda(r) of H(r) by the spatial Kaplan-Meier method |
raw |
the uncorrected estimate of H(r),
i.e. the empirical distribution of the distance from
a fixed point in the window to the nearest point of X
|
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
Baddeley, A.J. Spatial sampling and censoring. In O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. van Lieshout (eds) Stochastic Geometry: Likelihood and Computation. Chapman and Hall, 1998. Chapter 2, pages 37-78.
Baddeley, A.J. and Gill, R.D. The empty space hazard of a spatial pattern. Research Report 1994/3, Department of Mathematics, University of Western Australia, May 1994.
Hansen, M.B., Baddeley, A.J. and Gill, R.D. First contact distributions for spatial patterns: regularity and estimation. Advances in Applied Probability 31 (1999) 15-33.
Ripley, B.D. Statistical inference for spatial processes. Cambridge University Press, 1988.
Stoyan, D, Kendall, W.S. and Mecke, J. Stochastic geometry and its applications. 2nd edition. Springer Verlag, 1995.
X <- runifpoint(42) H <- Hest(X) Y <- rpoisline(10) H <- Hest(Y) data(heather) H <- Hest(heather$coarse)